Dynamics of a higher order rational difference equation

摘要

In this paper, we will investigate a nonlinear rational difference equation of higher order. Our concentration is on invariant intervals, periodic character, the character of semicycles and global asymptotic stability of all positive solutions ofxn+1=βxn+γxn-kBxn+Cxn-k,n=0,1,…It is worth to mention that our results solve the open problem proposed by Kulenvic and Ladas in their monograph [Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2002].